pacman::p_load(olsrr, ggstatsplot, ggpubr,
sf, spdep, GWmodel, tmap,
tidyverse, gtsummary, performance,
see, sfdep,corrplot)In-class_EX07
Getting Started
Importing the data
URA Master Plan 2014 planning subzone boundary
condo_resale = read_csv("data/aspatial/Condo_resale_2015.csv")Rows: 1436 Columns: 23
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
dbl (23): LATITUDE, LONGITUDE, POSTCODE, SELLING_PRICE, AREA_SQM, AGE, PROX_...
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.mpsz = st_read(dsn = "data/geospatial",
layer = "MP14_SUBZONE_WEB_PL")Reading layer `MP14_SUBZONE_WEB_PL' from data source
`/Users/yangyayong/Downloads/学校文件/smu文件/Term 3/G/yyyirene/ISSS626-GAA/In-class_EX/In-class_EX07/data/geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21mpsz <- read_rds("data/rds/mpsz.rds")condo_resale.sf <- st_as_sf(condo_resale,
coords = c("LONGITUDE", "LATITUDE"),
crs=4326) %>%
st_transform(crs=3414)corrplot(cor(condo_resale[, 5:23]), diag = FALSE, order = "AOE",
tl.pos = "td", tl.cex = 0.5, method = "number", type = "upper")
Correlation Analysis - ggstatsplot methods
ggcorrmat(condo_resale[,5:23])
Building a Hedonic Pricing Model by using Multiple Linear Regression Method
The code chunk below using lm() to calibrate the multiple linear regression model.
condo.mlr <- lm(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE +
PROX_URA_GROWTH_AREA + PROX_HAWKER_MARKET + PROX_KINDERGARTEN +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_TOP_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_SUPERMARKET +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale.sf) #using the sf version
summary(condo.mlr)
Call:
lm(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE +
PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_HAWKER_MARKET +
PROX_KINDERGARTEN + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_TOP_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_SUPERMARKET +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data = condo_resale.sf)
Residuals:
Min 1Q Median 3Q Max
-3475964 -293923 -23069 241043 12260381
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 481728.40 121441.01 3.967 7.65e-05 ***
AREA_SQM 12708.32 369.59 34.385 < 2e-16 ***
AGE -24440.82 2763.16 -8.845 < 2e-16 ***
PROX_CBD -78669.78 6768.97 -11.622 < 2e-16 ***
PROX_CHILDCARE -351617.91 109467.25 -3.212 0.00135 **
PROX_ELDERLYCARE 171029.42 42110.51 4.061 5.14e-05 ***
PROX_URA_GROWTH_AREA 38474.53 12523.57 3.072 0.00217 **
PROX_HAWKER_MARKET 23746.10 29299.76 0.810 0.41782
PROX_KINDERGARTEN 147468.99 82668.87 1.784 0.07466 .
PROX_MRT -314599.68 57947.44 -5.429 6.66e-08 ***
PROX_PARK 563280.50 66551.68 8.464 < 2e-16 ***
PROX_PRIMARY_SCH 180186.08 65237.95 2.762 0.00582 **
PROX_TOP_PRIMARY_SCH 2280.04 20410.43 0.112 0.91107
PROX_SHOPPING_MALL -206604.06 42840.60 -4.823 1.57e-06 ***
PROX_SUPERMARKET -44991.80 77082.64 -0.584 0.55953
PROX_BUS_STOP 683121.35 138353.28 4.938 8.85e-07 ***
NO_Of_UNITS -231.18 89.03 -2.597 0.00951 **
FAMILY_FRIENDLY 140340.77 47020.55 2.985 0.00289 **
FREEHOLD 359913.01 49220.22 7.312 4.38e-13 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 755800 on 1417 degrees of freedom
Multiple R-squared: 0.6518, Adjusted R-squared: 0.6474
F-statistic: 147.4 on 18 and 1417 DF, p-value: < 2.2e-16condo.mlr1 <- lm(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE +
PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK +
PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale.sf)
ols_regress(condo.mlr1) Model Summary
-----------------------------------------------------------------------------
R 0.807 RMSE 751998.679
R-Squared 0.651 MSE 571471422208.592
Adj. R-Squared 0.647 Coef. Var 43.168
Pred R-Squared 0.638 AIC 42966.758
MAE 414819.628 SBC 43051.072
-----------------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
--------------------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
--------------------------------------------------------------------------------
Regression 1.512586e+15 14 1.080418e+14 189.059 0.0000
Residual 8.120609e+14 1421 571471422208.592
Total 2.324647e+15 1435
--------------------------------------------------------------------------------
Parameter Estimates
-----------------------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
-----------------------------------------------------------------------------------------------------------------
(Intercept) 527633.222 108183.223 4.877 0.000 315417.244 739849.200
AREA_SQM 12777.523 367.479 0.584 34.771 0.000 12056.663 13498.382
AGE -24687.739 2754.845 -0.167 -8.962 0.000 -30091.739 -19283.740
PROX_CBD -77131.323 5763.125 -0.263 -13.384 0.000 -88436.469 -65826.176
PROX_CHILDCARE -318472.751 107959.512 -0.084 -2.950 0.003 -530249.889 -106695.613
PROX_ELDERLYCARE 185575.623 39901.864 0.090 4.651 0.000 107302.737 263848.510
PROX_URA_GROWTH_AREA 39163.254 11754.829 0.060 3.332 0.001 16104.571 62221.936
PROX_MRT -294745.107 56916.367 -0.112 -5.179 0.000 -406394.234 -183095.980
PROX_PARK 570504.807 65507.029 0.150 8.709 0.000 442003.938 699005.677
PROX_PRIMARY_SCH 159856.136 60234.599 0.062 2.654 0.008 41697.849 278014.424
PROX_SHOPPING_MALL -220947.251 36561.832 -0.115 -6.043 0.000 -292668.213 -149226.288
PROX_BUS_STOP 682482.221 134513.243 0.134 5.074 0.000 418616.359 946348.082
NO_Of_UNITS -245.480 87.947 -0.053 -2.791 0.005 -418.000 -72.961
FAMILY_FRIENDLY 146307.576 46893.021 0.057 3.120 0.002 54320.593 238294.560
FREEHOLD 350599.812 48506.485 0.136 7.228 0.000 255447.802 445751.821
-----------------------------------------------------------------------------------------------------------------Model Assessment: olsrr method
In this section, we would like to introduce you a fantastic R package specially programmed for performing OLS regression. It is called olsrr. It provides a collection of very useful methods for building better multiple linear regression models:
comprehensive regression output
residual diagnostics
measures of influence
heteroskedasticity tests
model fit assessment
variable contribution assessment
variable selection procedures
Generating tidy linear regression report
ols_regress(condo.mlr) Model Summary
-----------------------------------------------------------------------------
R 0.807 RMSE 750799.558
R-Squared 0.652 MSE 571258408962.150
Adj. R-Squared 0.647 Coef. Var 43.160
Pred R-Squared 0.637 AIC 42970.175
MAE 413425.809 SBC 43075.567
-----------------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
--------------------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
--------------------------------------------------------------------------------
Regression 1.515174e+15 18 8.417631e+13 147.352 0.0000
Residual 8.094732e+14 1417 571258408962.150
Total 2.324647e+15 1435
--------------------------------------------------------------------------------
Parameter Estimates
-----------------------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
-----------------------------------------------------------------------------------------------------------------
(Intercept) 481728.405 121441.014 3.967 0.000 243504.909 719951.900
AREA_SQM 12708.324 369.590 0.580 34.385 0.000 11983.322 13433.326
AGE -24440.816 2763.164 -0.165 -8.845 0.000 -29861.148 -19020.484
PROX_CBD -78669.779 6768.972 -0.268 -11.622 0.000 -91948.061 -65391.496
PROX_CHILDCARE -351617.910 109467.252 -0.092 -3.212 0.001 -566353.201 -136882.619
PROX_ELDERLYCARE 171029.418 42110.506 0.083 4.061 0.000 88423.783 253635.053
PROX_URA_GROWTH_AREA 38474.534 12523.567 0.059 3.072 0.002 13907.809 63041.258
PROX_HAWKER_MARKET 23746.098 29299.755 0.019 0.810 0.418 -33729.461 81221.657
PROX_KINDERGARTEN 147468.986 82668.868 0.031 1.784 0.075 -14697.534 309635.506
PROX_MRT -314599.679 57947.441 -0.120 -5.429 0.000 -428271.672 -200927.687
PROX_PARK 563280.499 66551.675 0.148 8.464 0.000 432730.102 693830.897
PROX_PRIMARY_SCH 180186.083 65237.948 0.070 2.762 0.006 52212.744 308159.421
PROX_TOP_PRIMARY_SCH 2280.036 20410.435 0.002 0.112 0.911 -37757.880 42317.951
PROX_SHOPPING_MALL -206604.057 42840.595 -0.108 -4.823 0.000 -290641.863 -122566.252
PROX_SUPERMARKET -44991.803 77082.635 -0.012 -0.584 0.560 -196200.149 106216.542
PROX_BUS_STOP 683121.347 138353.278 0.134 4.938 0.000 411722.087 954520.608
NO_Of_UNITS -231.180 89.033 -0.050 -2.597 0.010 -405.830 -56.530
FAMILY_FRIENDLY 140340.770 47020.551 0.055 2.985 0.003 48103.399 232578.141
FREEHOLD 359913.008 49220.224 0.140 7.312 0.000 263360.671 456465.345
-----------------------------------------------------------------------------------------------------------------ols_vif_tol(condo.mlr) Variables Tolerance VIF
1 AREA_SQM 0.8625928 1.159296
2 AGE 0.7026139 1.423257
3 PROX_CBD 0.4605774 2.171188
4 PROX_CHILDCARE 0.2981029 3.354546
5 PROX_ELDERLYCARE 0.5922259 1.688545
6 PROX_URA_GROWTH_AREA 0.6614127 1.511915
7 PROX_HAWKER_MARKET 0.4373889 2.286295
8 PROX_KINDERGARTEN 0.8370845 1.194622
9 PROX_MRT 0.5049530 1.980382
10 PROX_PARK 0.8018396 1.247132
11 PROX_PRIMARY_SCH 0.3855782 2.593508
12 PROX_TOP_PRIMARY_SCH 0.4968645 2.012621
13 PROX_SHOPPING_MALL 0.4906426 2.038144
14 PROX_SUPERMARKET 0.6152063 1.625471
15 PROX_BUS_STOP 0.3320516 3.011580
16 NO_Of_UNITS 0.6731165 1.485627
17 FAMILY_FRIENDLY 0.7202230 1.388459
18 FREEHOLD 0.6729095 1.486084condo_fw_mlr <- ols_step_forward_p(
condo.mlr,
p_val = 0.05,
details = FALSE
)plot(condo_fw_mlr)
Visualising model parameters
ggcoefstats(condo.mlr,
sort = "ascending")Number of labels is greater than default palette color count.
• Select another color `palette` (and/or `package`).
Test for Non-Linearity
In multiple linear regression, it is important for us to test the assumption that linearity and additivity of the relationship between dependent and independent variables.
In the code chunk below, the ols_plot_resid_fit() of olsrr package is used to perform linearity assumption test.
ols_plot_resid_fit(condo_fw_mlr$model)
The figure above reveals that most of the data poitns are scattered around the 0 line, hence we can safely conclude that the relationships between the dependent variable and independent variables are linear.
Test for Normality Assumption
Lastly, the code chunk below uses ols_plot_resid_hist() of olsrr package to perform normality assumption test.
ols_plot_resid_hist(condo_fw_mlr$model)
The figure reveals that the residual of the multiple linear regression model (i.e. condo.mlr1) is resemble normal distribution.
If you prefer formal statistical test methods, the ols_test_normality() of olsrr package can be used as shown in the code chun below.
ols_test_normality(condo_fw_mlr$model)Warning in ks.test.default(y, "pnorm", mean(y), sd(y)): ties should not be
present for the one-sample Kolmogorov-Smirnov test-----------------------------------------------
Test Statistic pvalue
-----------------------------------------------
Shapiro-Wilk 0.6856 0.0000
Kolmogorov-Smirnov 0.1366 0.0000
Cramer-von Mises 121.0768 0.0000
Anderson-Darling 67.9551 0.0000
-----------------------------------------------The summary table above reveals that the p-values of the four tests are way smaller than the alpha value of 0.05. Hence we will reject the null hypothesis and infer that there is statistical evidence that the residual are not normally distributed.
Testing for Spatial Autocorrelation
The hedonic model we try to build are using geographically referenced attributes, hence it is also important for us to visual the residual of the hedonic pricing model.
First, we will export the residual of the hedonic pricing model and save it as a data frame.
mlr_output <- as.data.frame(condo_fw_mlr$model$residuals) %>%
rename(`FW_MLR_RES` = `condo_fw_mlr$model$residuals`)Next, we will join the newly created data frame with condo_resale.sf object.
condo_resale.sf <- cbind(condo_resale.sf,
mlr_output$FW_MLR_RES) %>%
rename(`MLR_RES` = `mlr_output.FW_MLR_RES`)Next, we will use tmap package to display the distribution of the residuals on an interactive map.
The code churn below will turn on the interactive mode of tmap.
tmap_mode("view")tmap mode set to interactive viewingtm_shape(mpsz)+
tmap_options(check.and.fix = TRUE) +
tm_polygons(alpha = 0.4) +
tm_shape(condo_resale.sf) +
tm_dots(col = "MLR_RES",
alpha = 0.6,
style="quantile")Warning: The shape mpsz is invalid (after reprojection). See sf::st_is_validVariable(s) "MLR_RES" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.The figure shows the visualization of spatial data, where the colors represent different MLR_RES (multiple linear regression residual values), which are used to analyze the existence of spatial autocorrelation. Spatial autocorrelation refers to the similarity or correlation between adjacent areas in geographic space, that is, “near things are more similar than distant things.”
In this figure, you can judge the existence of spatial autocorrelation by the following aspects:
Color aggregation phenomenon:
The figure shows that different areas use different colors to represent residual values, and the colors change from yellow (negative residual values) to green (positive residual values). If close areas in space show similar colors (i.e. similar residual values), then this indicates the existence of positive spatial autocorrelation. For example, the yellow points in some areas of the figure are concentrated together, and the green points are also concentrated in some areas, indicating that the adjacent areas have certain similarities in residual values. Geographical concentration:
If some colors are obviously concentrated in a specific geographic area and are not randomly distributed, this concentrated distribution suggests the existence of autocorrelation. For example, the multiple green points in the figure are concentrated in the central and eastern areas of the map, indicating that the property prices in these areas have similar trends or patterns. Statistical analysis of spatial autocorrelation:
Usually, to rigorously determine spatial autocorrelation, researchers use statistical methods (such as Morans’ I) to quantify the strength of autocorrelation. This method can calculate the significance of spatial autocorrelation by the spatial distribution of residuals, but the figure has been initially visualized to show this possible trend. Therefore, spatial autocorrelation can be identified by the spatial distribution pattern of these colors, and the clustering of different color areas in the figure is a potential sign of spatial autocorrelation.
tmap_mode("plot")tmap mode set to plottingThe figure above reveal that there is sign of spatial autocorrelation.
Spatial stationary test
To proof that our observation is indeed true, the Moran’s I test will be performed
Ho: The residuals are randomly distributed (also known as spatial stationary) H1: The residuals are spatially non-stationary
First, we will compute the distance-based weight matrix by using dnearneigh() function of spdep.
condo_resale.sf <- condo_resale.sf %>%
mutate(nb = st_knn(geometry, k=6,
longlat = FALSE),
wt = st_weights(nb,
style = "W"),
.before = 1)Next, global_moran_perm() of sfdep is used to perform global Moran permutation test.
global_moran_perm(condo_resale.sf$MLR_RES,
condo_resale.sf$nb,
condo_resale.sf$wt,
alternative = "two.sided",
nsim = 99)
Monte-Carlo simulation of Moran I
data: x
weights: listw
number of simulations + 1: 100
statistic = 0.32254, observed rank = 100, p-value < 2.2e-16
alternative hypothesis: two.sidedSince the Observed Global Moran I = 0.25586 which is greater than 0, we can infer than the residuals resemble cluster distribution.
Building Hedonic Pricing Models using GWmodel
In this section, you are going to learn how to modelling hedonic pricing by using geographically weighted regression model. Two spatial weights will be used, they are: fixed and adaptive bandwidth schemes.
Building Fixed Bandwidth GWR Model
Computing fixed bandwith
In the code chunk below bw.gwr() of GWModel package is used to determine the optimal fixed bandwidth to use in the model. Notice that the argument adaptive is set to FALSE indicates that we are interested to compute the fixed bandwidth.
There are two possible approaches can be uused to determine the stopping rule, they are: CV cross-validation approach and AIC corrected (AICc) approach. We define the stopping rule using approach agreement.
bw_fixed <- bw.gwr(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE +
PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_SHOPPING_MALL + PROX_BUS_STOP +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale.sf,
approach="CV",
kernel="gaussian",
adaptive=FALSE,
longlat=FALSE)Fixed bandwidth: 17660.96 CV score: 8.259118e+14
Fixed bandwidth: 10917.26 CV score: 7.970454e+14
Fixed bandwidth: 6749.419 CV score: 7.273273e+14
Fixed bandwidth: 4173.553 CV score: 6.300006e+14
Fixed bandwidth: 2581.58 CV score: 5.404958e+14
Fixed bandwidth: 1597.687 CV score: 4.857515e+14
Fixed bandwidth: 989.6077 CV score: 4.722431e+14
Fixed bandwidth: 613.7939 CV score: 1.379526e+16
Fixed bandwidth: 1221.873 CV score: 4.778717e+14
Fixed bandwidth: 846.0596 CV score: 4.791629e+14
Fixed bandwidth: 1078.325 CV score: 4.751406e+14
Fixed bandwidth: 934.7772 CV score: 4.72518e+14
Fixed bandwidth: 1023.495 CV score: 4.730305e+14
Fixed bandwidth: 968.6643 CV score: 4.721317e+14
Fixed bandwidth: 955.7206 CV score: 4.722072e+14
Fixed bandwidth: 976.6639 CV score: 4.721387e+14
Fixed bandwidth: 963.7202 CV score: 4.721484e+14
Fixed bandwidth: 971.7199 CV score: 4.721293e+14
Fixed bandwidth: 973.6083 CV score: 4.721309e+14
Fixed bandwidth: 970.5527 CV score: 4.721295e+14
Fixed bandwidth: 972.4412 CV score: 4.721296e+14
Fixed bandwidth: 971.2741 CV score: 4.721292e+14
Fixed bandwidth: 970.9985 CV score: 4.721293e+14
Fixed bandwidth: 971.4443 CV score: 4.721292e+14
Fixed bandwidth: 971.5496 CV score: 4.721293e+14
Fixed bandwidth: 971.3793 CV score: 4.721292e+14
Fixed bandwidth: 971.3391 CV score: 4.721292e+14
Fixed bandwidth: 971.3143 CV score: 4.721292e+14
Fixed bandwidth: 971.3545 CV score: 4.721292e+14
Fixed bandwidth: 971.3296 CV score: 4.721292e+14
Fixed bandwidth: 971.345 CV score: 4.721292e+14
Fixed bandwidth: 971.3355 CV score: 4.721292e+14
Fixed bandwidth: 971.3413 CV score: 4.721292e+14
Fixed bandwidth: 971.3377 CV score: 4.721292e+14
Fixed bandwidth: 971.34 CV score: 4.721292e+14
Fixed bandwidth: 971.3405 CV score: 4.721292e+14
Fixed bandwidth: 971.3396 CV score: 4.721292e+14
Fixed bandwidth: 971.3402 CV score: 4.721292e+14
Fixed bandwidth: 971.3398 CV score: 4.721292e+14
Fixed bandwidth: 971.34 CV score: 4.721292e+14
Fixed bandwidth: 971.3399 CV score: 4.721292e+14
Fixed bandwidth: 971.34 CV score: 4.721292e+14 The result shows that the recommended bandwidth is 971.3405 metres.
Spatial analysis context: When analyzing spatial data, distances between points or areas are usually expressed in meters or kilometers. Therefore, any smoothing or kernel density calculations will use bandwidth values corresponding to these units. Geographic projections: If the spatial data is projected into a coordinate system such as UTM (Universal Transverse Mercator), which uses meters as a unit of measurement, then the bandwidth, as a distance value, is naturally expressed in meters.
GWModel method - fixed bandwith
Now we can use the code chunk below to calibrate the gwr model using fixed bandwidth and gaussian kernel.
gwr_fixed <- gwr.basic(formula = SELLING_PRICE ~ AREA_SQM +
AGE + PROX_CBD + PROX_CHILDCARE +
PROX_ELDERLYCARE +PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_SHOPPING_MALL + PROX_BUS_STOP +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale.sf,
bw=bw_fixed,
kernel = 'gaussian',
longlat = FALSE)gwr_fixed ***********************************************************************
* Package GWmodel *
***********************************************************************
Program starts at: 2024-11-10 11:09:52.918668
Call:
gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD +
PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data = condo_resale.sf, bw = bw_fixed, kernel = "gaussian",
longlat = FALSE)
Dependent (y) variable: SELLING_PRICE
Independent variables: AREA_SQM AGE PROX_CBD PROX_CHILDCARE PROX_ELDERLYCARE PROX_URA_GROWTH_AREA PROX_MRT PROX_PARK PROX_PRIMARY_SCH PROX_SHOPPING_MALL PROX_BUS_STOP NO_Of_UNITS FAMILY_FRIENDLY FREEHOLD
Number of data points: 1436
***********************************************************************
* Results of Global Regression *
***********************************************************************
Call:
lm(formula = formula, data = data)
Residuals:
Min 1Q Median 3Q Max
-3470778 -298119 -23481 248917 12234210
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 527633.22 108183.22 4.877 1.20e-06 ***
AREA_SQM 12777.52 367.48 34.771 < 2e-16 ***
AGE -24687.74 2754.84 -8.962 < 2e-16 ***
PROX_CBD -77131.32 5763.12 -13.384 < 2e-16 ***
PROX_CHILDCARE -318472.75 107959.51 -2.950 0.003231 **
PROX_ELDERLYCARE 185575.62 39901.86 4.651 3.61e-06 ***
PROX_URA_GROWTH_AREA 39163.25 11754.83 3.332 0.000885 ***
PROX_MRT -294745.11 56916.37 -5.179 2.56e-07 ***
PROX_PARK 570504.81 65507.03 8.709 < 2e-16 ***
PROX_PRIMARY_SCH 159856.14 60234.60 2.654 0.008046 **
PROX_SHOPPING_MALL -220947.25 36561.83 -6.043 1.93e-09 ***
PROX_BUS_STOP 682482.22 134513.24 5.074 4.42e-07 ***
NO_Of_UNITS -245.48 87.95 -2.791 0.005321 **
FAMILY_FRIENDLY 146307.58 46893.02 3.120 0.001845 **
FREEHOLD 350599.81 48506.48 7.228 7.98e-13 ***
---Significance stars
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 756000 on 1421 degrees of freedom
Multiple R-squared: 0.6507
Adjusted R-squared: 0.6472
F-statistic: 189.1 on 14 and 1421 DF, p-value: < 2.2e-16
***Extra Diagnostic information
Residual sum of squares: 8.120609e+14
Sigma(hat): 752522.9
AIC: 42966.76
AICc: 42967.14
BIC: 41731.39
***********************************************************************
* Results of Geographically Weighted Regression *
***********************************************************************
*********************Model calibration information*********************
Kernel function: gaussian
Fixed bandwidth: 971.34
Regression points: the same locations as observations are used.
Distance metric: Euclidean distance metric is used.
****************Summary of GWR coefficient estimates:******************
Min. 1st Qu. Median 3rd Qu.
Intercept -3.5988e+07 -5.1998e+05 7.6780e+05 1.7412e+06
AREA_SQM 1.0003e+03 5.2758e+03 7.4740e+03 1.2301e+04
AGE -1.3475e+05 -2.0813e+04 -8.6260e+03 -3.7784e+03
PROX_CBD -7.7047e+07 -2.3608e+05 -8.3599e+04 3.4646e+04
PROX_CHILDCARE -6.0097e+06 -3.3667e+05 -9.7426e+04 2.9007e+05
PROX_ELDERLYCARE -3.5001e+06 -1.5970e+05 3.1970e+04 1.9577e+05
PROX_URA_GROWTH_AREA -3.0170e+06 -8.2013e+04 7.0749e+04 2.2612e+05
PROX_MRT -3.5282e+06 -6.5836e+05 -1.8833e+05 3.6922e+04
PROX_PARK -1.2062e+06 -2.1732e+05 3.5383e+04 4.1335e+05
PROX_PRIMARY_SCH -2.2695e+07 -1.7066e+05 4.8472e+04 5.1555e+05
PROX_SHOPPING_MALL -7.2585e+06 -1.6684e+05 -1.0517e+04 1.5923e+05
PROX_BUS_STOP -1.4676e+06 -4.5207e+04 3.7601e+05 1.1664e+06
NO_Of_UNITS -1.3170e+03 -2.4822e+02 -3.0846e+01 2.5496e+02
FAMILY_FRIENDLY -2.2749e+06 -1.1140e+05 7.6214e+03 1.6107e+05
FREEHOLD -9.2067e+06 3.8074e+04 1.5169e+05 3.7528e+05
Max.
Intercept 112794435
AREA_SQM 21575
AGE 434203
PROX_CBD 2704604
PROX_CHILDCARE 1654086
PROX_ELDERLYCARE 38867861
PROX_URA_GROWTH_AREA 78515805
PROX_MRT 3124325
PROX_PARK 18122439
PROX_PRIMARY_SCH 4637517
PROX_SHOPPING_MALL 1529953
PROX_BUS_STOP 11342209
NO_Of_UNITS 12907
FAMILY_FRIENDLY 1720745
FREEHOLD 6073642
************************Diagnostic information*************************
Number of data points: 1436
Effective number of parameters (2trace(S) - trace(S'S)): 438.3807
Effective degrees of freedom (n-2trace(S) + trace(S'S)): 997.6193
AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 42263.61
AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 41632.36
BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 42515.71
Residual sum of squares: 2.534069e+14
R-square value: 0.8909912
Adjusted R-square value: 0.8430418
***********************************************************************
Program stops at: 2024-11-10 11:09:53.407016 Building Adaptive Bandwidth GWR Model
In this section, we will calibrate the gwr-based hedonic pricing model by using adaptive bandwidth approach.
Computing the adaptive bandwidth
Similar to the earlier section, we will first use bw.gwr() to determine the recommended data point to use.
The code chunk used look very similar to the one used to compute the fixed bandwidth except the adaptive argument has changed to TRUE.
bw_adaptive <- bw.gwr(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE +
PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK +
PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale.sf,
approach="CV",
kernel="gaussian",
adaptive=TRUE,
longlat=FALSE)Adaptive bandwidth: 895 CV score: 7.952401e+14
Adaptive bandwidth: 561 CV score: 7.667364e+14
Adaptive bandwidth: 354 CV score: 6.953454e+14
Adaptive bandwidth: 226 CV score: 6.15223e+14
Adaptive bandwidth: 147 CV score: 5.674373e+14
Adaptive bandwidth: 98 CV score: 5.426745e+14
Adaptive bandwidth: 68 CV score: 5.168117e+14
Adaptive bandwidth: 49 CV score: 4.859631e+14
Adaptive bandwidth: 37 CV score: 4.646518e+14
Adaptive bandwidth: 30 CV score: 4.422088e+14
Adaptive bandwidth: 25 CV score: 4.430816e+14
Adaptive bandwidth: 32 CV score: 4.505602e+14
Adaptive bandwidth: 27 CV score: 4.462172e+14
Adaptive bandwidth: 30 CV score: 4.422088e+14 The result shows that the 30 is the recommended data points to be used.
Constructing the adaptive bandwidth gwr model
Now, we can go ahead to calibrate the gwr-based hedonic pricing model by using adaptive bandwidth and gaussian kernel as shown in the code chunk below.
gwr_adaptive <- gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE +
PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK +
PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale.sf,
bw=bw_adaptive,
kernel = 'gaussian',
adaptive=TRUE,
longlat = FALSE)gwr_adaptive ***********************************************************************
* Package GWmodel *
***********************************************************************
Program starts at: 2024-11-10 11:09:57.45913
Call:
gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD +
PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data = condo_resale.sf, bw = bw_adaptive, kernel = "gaussian",
adaptive = TRUE, longlat = FALSE)
Dependent (y) variable: SELLING_PRICE
Independent variables: AREA_SQM AGE PROX_CBD PROX_CHILDCARE PROX_ELDERLYCARE PROX_URA_GROWTH_AREA PROX_MRT PROX_PARK PROX_PRIMARY_SCH PROX_SHOPPING_MALL PROX_BUS_STOP NO_Of_UNITS FAMILY_FRIENDLY FREEHOLD
Number of data points: 1436
***********************************************************************
* Results of Global Regression *
***********************************************************************
Call:
lm(formula = formula, data = data)
Residuals:
Min 1Q Median 3Q Max
-3470778 -298119 -23481 248917 12234210
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 527633.22 108183.22 4.877 1.20e-06 ***
AREA_SQM 12777.52 367.48 34.771 < 2e-16 ***
AGE -24687.74 2754.84 -8.962 < 2e-16 ***
PROX_CBD -77131.32 5763.12 -13.384 < 2e-16 ***
PROX_CHILDCARE -318472.75 107959.51 -2.950 0.003231 **
PROX_ELDERLYCARE 185575.62 39901.86 4.651 3.61e-06 ***
PROX_URA_GROWTH_AREA 39163.25 11754.83 3.332 0.000885 ***
PROX_MRT -294745.11 56916.37 -5.179 2.56e-07 ***
PROX_PARK 570504.81 65507.03 8.709 < 2e-16 ***
PROX_PRIMARY_SCH 159856.14 60234.60 2.654 0.008046 **
PROX_SHOPPING_MALL -220947.25 36561.83 -6.043 1.93e-09 ***
PROX_BUS_STOP 682482.22 134513.24 5.074 4.42e-07 ***
NO_Of_UNITS -245.48 87.95 -2.791 0.005321 **
FAMILY_FRIENDLY 146307.58 46893.02 3.120 0.001845 **
FREEHOLD 350599.81 48506.48 7.228 7.98e-13 ***
---Significance stars
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 756000 on 1421 degrees of freedom
Multiple R-squared: 0.6507
Adjusted R-squared: 0.6472
F-statistic: 189.1 on 14 and 1421 DF, p-value: < 2.2e-16
***Extra Diagnostic information
Residual sum of squares: 8.120609e+14
Sigma(hat): 752522.9
AIC: 42966.76
AICc: 42967.14
BIC: 41731.39
***********************************************************************
* Results of Geographically Weighted Regression *
***********************************************************************
*********************Model calibration information*********************
Kernel function: gaussian
Adaptive bandwidth: 30 (number of nearest neighbours)
Regression points: the same locations as observations are used.
Distance metric: Euclidean distance metric is used.
****************Summary of GWR coefficient estimates:******************
Min. 1st Qu. Median 3rd Qu.
Intercept -1.3487e+08 -2.4669e+05 7.7928e+05 1.6194e+06
AREA_SQM 3.3188e+03 5.6285e+03 7.7825e+03 1.2738e+04
AGE -9.6746e+04 -2.9288e+04 -1.4043e+04 -5.6119e+03
PROX_CBD -2.5330e+06 -1.6256e+05 -7.7242e+04 2.6624e+03
PROX_CHILDCARE -1.2790e+06 -2.0175e+05 8.7158e+03 3.7778e+05
PROX_ELDERLYCARE -1.6212e+06 -9.2050e+04 6.1029e+04 2.8184e+05
PROX_URA_GROWTH_AREA -7.2686e+06 -3.0350e+04 4.5869e+04 2.4613e+05
PROX_MRT -4.3781e+07 -6.7282e+05 -2.2115e+05 -7.4593e+04
PROX_PARK -2.9020e+06 -1.6782e+05 1.1601e+05 4.6572e+05
PROX_PRIMARY_SCH -8.6418e+05 -1.6627e+05 -7.7853e+03 4.3222e+05
PROX_SHOPPING_MALL -1.8272e+06 -1.3175e+05 -1.4049e+04 1.3799e+05
PROX_BUS_STOP -2.0579e+06 -7.1461e+04 4.1104e+05 1.2071e+06
NO_Of_UNITS -2.1993e+03 -2.3685e+02 -3.4699e+01 1.1657e+02
FAMILY_FRIENDLY -5.9879e+05 -5.0927e+04 2.6173e+04 2.2481e+05
FREEHOLD -1.6340e+05 4.0765e+04 1.9023e+05 3.7960e+05
Max.
Intercept 18758355
AREA_SQM 23064
AGE 13303
PROX_CBD 11346650
PROX_CHILDCARE 2892127
PROX_ELDERLYCARE 2465671
PROX_URA_GROWTH_AREA 7384059
PROX_MRT 1186242
PROX_PARK 2588497
PROX_PRIMARY_SCH 3381462
PROX_SHOPPING_MALL 38038564
PROX_BUS_STOP 12081592
NO_Of_UNITS 1010
FAMILY_FRIENDLY 2072414
FREEHOLD 1813995
************************Diagnostic information*************************
Number of data points: 1436
Effective number of parameters (2trace(S) - trace(S'S)): 350.3088
Effective degrees of freedom (n-2trace(S) + trace(S'S)): 1085.691
AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 41982.22
AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 41546.74
BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 41914.08
Residual sum of squares: 2.528227e+14
R-square value: 0.8912425
Adjusted R-square value: 0.8561185
***********************************************************************
Program stops at: 2024-11-10 11:09:58.031979 The report shows that the AICc the adaptive distance gwr is 41982.22 which is even smaller than the AICc of the fixed distance gwr of 42263.61.
Visualising GWR Output
In addition to regression residuals, the output feature class table includes fields for observed and predicted y values, condition number (cond), Local R2, residuals, and explanatory variable coefficients and standard errors:
Condition Number: this diagnostic evaluates local collinearity. In the presence of strong local collinearity, results become unstable. Results associated with condition numbers larger than 30, may be unreliable.
Local R2: these values range between 0.0 and 1.0 and indicate how well the local regression model fits observed y values. Very low values indicate the local model is performing poorly. Mapping the Local R2 values to see where GWR predicts well and where it predicts poorly may provide clues about important variables that may be missing from the regression model.
Predicted: these are the estimated (or fitted) y values 3. computed by GWR.
Residuals: to obtain the residual values, the fitted y values are subtracted from the observed y values. Standardized residuals have a mean of zero and a standard deviation of 1. A cold-to-hot rendered map of standardized residuals can be produce by using these values.
Coefficient Standard Error: these values measure the reliability of each coefficient estimate. Confidence in those estimates are higher when standard errors are small in relation to the actual coefficient values. Large standard errors may indicate problems with local collinearity.
They are all stored in a SpatialPointsDataFrame or SpatialPolygonsDataFrame object integrated with fit.points, GWR coefficient estimates, y value, predicted values, coefficient standard errors and t-values in its “data” slot in an object called SDF of the output list.
Converting SDF into sf data.frame
To visualise the fields in SDF, we need to first covert it into sf data.frame by using the code chunk below.
gwr_adaptive_output <- as.data.frame(
gwr_adaptive$SDF) %>%
select(-c(2:15))gwr_sf_adaptive <- cbind(condo_resale.sf,
gwr_adaptive_output)Next, glimpse() is used to display the content of condo_resale_sf.adaptive sf data frame.
glimpse(gwr_sf_adaptive)Rows: 1,436
Columns: 63
$ nb <nb> <66, 77, 123, 238, 239, 343>, <21, 162, 163, 19…
$ wt <list> <0.1666667, 0.1666667, 0.1666667, 0.1666667, …
$ POSTCODE <dbl> 118635, 288420, 267833, 258380, 467169, 466472…
$ SELLING_PRICE <dbl> 3000000, 3880000, 3325000, 4250000, 1400000, 1…
$ AREA_SQM <dbl> 309, 290, 248, 127, 145, 139, 218, 141, 165, 1…
$ AGE <dbl> 30, 32, 33, 7, 28, 22, 24, 24, 27, 31, 17, 22,…
$ PROX_CBD <dbl> 7.941259, 6.609797, 6.898000, 4.038861, 11.783…
$ PROX_CHILDCARE <dbl> 0.16597932, 0.28027246, 0.42922669, 0.39473543…
$ PROX_ELDERLYCARE <dbl> 2.5198118, 1.9333338, 0.5021395, 1.9910316, 1.…
$ PROX_URA_GROWTH_AREA <dbl> 6.618741, 7.505109, 6.463887, 4.906512, 6.4106…
$ PROX_HAWKER_MARKET <dbl> 1.76542207, 0.54507614, 0.37789301, 1.68259969…
$ PROX_KINDERGARTEN <dbl> 0.05835552, 0.61592412, 0.14120309, 0.38200076…
$ PROX_MRT <dbl> 0.5607188, 0.6584461, 0.3053433, 0.6910183, 0.…
$ PROX_PARK <dbl> 1.1710446, 0.1992269, 0.2779886, 0.9832843, 0.…
$ PROX_PRIMARY_SCH <dbl> 1.6340256, 0.9747834, 1.4715016, 1.4546324, 0.…
$ PROX_TOP_PRIMARY_SCH <dbl> 3.3273195, 0.9747834, 1.4715016, 2.3006394, 0.…
$ PROX_SHOPPING_MALL <dbl> 2.2102717, 2.9374279, 1.2256850, 0.3525671, 1.…
$ PROX_SUPERMARKET <dbl> 0.9103958, 0.5900617, 0.4135583, 0.4162219, 0.…
$ PROX_BUS_STOP <dbl> 0.10336166, 0.28673408, 0.28504777, 0.29872340…
$ NO_Of_UNITS <dbl> 18, 20, 27, 30, 30, 31, 32, 32, 32, 32, 34, 34…
$ FAMILY_FRIENDLY <dbl> 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0…
$ FREEHOLD <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1…
$ LEASEHOLD_99YR <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ MLR_RES <dbl> -1489099.55, 415494.57, 194129.69, 1088992.71,…
$ Intercept <dbl> 2050011.67, 1633128.24, 3433608.17, 234358.91,…
$ y <dbl> 3000000, 3880000, 3325000, 4250000, 1400000, 1…
$ yhat <dbl> 2886531.8, 3466801.5, 3616527.2, 5435481.6, 13…
$ residual <dbl> 113468.16, 413198.52, -291527.20, -1185481.63,…
$ CV_Score <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ Stud_residual <dbl> 0.38207013, 1.01433140, -0.83780678, -2.846146…
$ Intercept_SE <dbl> 516105.5, 488083.5, 963711.4, 444185.5, 211962…
$ AREA_SQM_SE <dbl> 823.2860, 825.2380, 988.2240, 617.4007, 1376.2…
$ AGE_SE <dbl> 5889.782, 6226.916, 6510.236, 6010.511, 8180.3…
$ PROX_CBD_SE <dbl> 37411.22, 23615.06, 56103.77, 469337.41, 41064…
$ PROX_CHILDCARE_SE <dbl> 319111.1, 299705.3, 349128.5, 304965.2, 698720…
$ PROX_ELDERLYCARE_SE <dbl> 120633.34, 84546.69, 129687.07, 127150.69, 327…
$ PROX_URA_GROWTH_AREA_SE <dbl> 56207.39, 76956.50, 95774.60, 470762.12, 47433…
$ PROX_MRT_SE <dbl> 185181.3, 281133.9, 275483.7, 279877.1, 363830…
$ PROX_PARK_SE <dbl> 205499.6, 229358.7, 314124.3, 227249.4, 364580…
$ PROX_PRIMARY_SCH_SE <dbl> 152400.7, 165150.7, 196662.6, 240878.9, 249087…
$ PROX_SHOPPING_MALL_SE <dbl> 109268.8, 98906.8, 119913.3, 177104.1, 301032.…
$ PROX_BUS_STOP_SE <dbl> 600668.6, 410222.1, 464156.7, 562810.8, 740922…
$ NO_Of_UNITS_SE <dbl> 218.1258, 208.9410, 210.9828, 361.7767, 299.50…
$ FAMILY_FRIENDLY_SE <dbl> 131474.73, 114989.07, 146607.22, 108726.62, 16…
$ FREEHOLD_SE <dbl> 115954.0, 130110.0, 141031.5, 138239.1, 210641…
$ Intercept_TV <dbl> 3.9720784, 3.3460017, 3.5629010, 0.5276150, 1.…
$ AREA_SQM_TV <dbl> 11.614302, 20.087361, 13.247868, 33.577223, 4.…
$ AGE_TV <dbl> -1.6154474, -9.3441881, -4.1023685, -15.524301…
$ PROX_CBD_TV <dbl> -3.22582173, -6.32792021, -4.62353528, 5.17080…
$ PROX_CHILDCARE_TV <dbl> 1.000488185, 1.471786337, -0.344047555, 1.5766…
$ PROX_ELDERLYCARE_TV <dbl> -3.26126929, 3.84626245, 4.13191383, 2.4756745…
$ PROX_URA_GROWTH_AREA_TV <dbl> -2.846248368, -1.848971738, -2.648105057, -5.6…
$ PROX_MRT_TV <dbl> -1.61864578, -8.92998600, -3.40075727, -7.2870…
$ PROX_PARK_TV <dbl> -0.83749312, 2.28192684, 0.66565951, -3.340617…
$ PROX_PRIMARY_SCH_TV <dbl> 1.59230221, 6.70194543, 2.90580089, 12.9836104…
$ PROX_SHOPPING_MALL_TV <dbl> 2.753588422, -0.886626400, -1.056869486, -0.16…
$ PROX_BUS_STOP_TV <dbl> 2.0154464, 4.4941192, 3.0419145, 12.8383775, 0…
$ NO_Of_UNITS_TV <dbl> 0.480589953, -1.380026395, -0.045279967, -0.44…
$ FAMILY_FRIENDLY_TV <dbl> -0.06902748, 2.69655779, 0.04058290, 14.312764…
$ FREEHOLD_TV <dbl> 2.6213469, 3.0452799, 1.1970499, 8.7711485, 1.…
$ Local_R2 <dbl> 0.8846744, 0.8899773, 0.8947007, 0.9073605, 0.…
$ geometry <POINT [m]> POINT (22085.12 29951.54), POINT (25656.…
$ geometry.1 <POINT [m]> POINT (22085.12 29951.54), POINT (25656.…summary(gwr_adaptive$SDF$yhat) Min. 1st Qu. Median Mean 3rd Qu. Max.
171347 1102001 1385528 1751842 1982307 13887901 Visualising local R2
The code chunks below is used to create an interactive point symbol map.
tmap_mode("view")tmap mode set to interactive viewingtmap_options(check.and.fix = TRUE)
tm_shape(mpsz)+
tm_polygons(alpha = 0.1) +
tm_shape(gwr_sf_adaptive) +
tm_dots(col = "Local_R2",
border.col = "gray60",
border.lwd = 1) +
tm_view(set.zoom.limits = c(11,14))Warning: The shape mpsz is invalid (after reprojection). See sf::st_is_validtmap_mode("plot")tmap mode set to plottingVisualising coefficient estimates
The code chunks below is used to create an interactive point symbol map.
tmap_options(check.and.fix = TRUE)
tmap_mode("view")tmap mode set to interactive viewingAREA_SQM_SE <- tm_shape(mpsz)+
tm_polygons(alpha = 0.1) +
tm_shape(gwr_sf_adaptive) +
tm_dots(col = "AREA_SQM_SE",
border.col = "gray60",
border.lwd = 1) +
tm_view(set.zoom.limits = c(11,14))
AREA_SQM_TV <- tm_shape(mpsz)+
tm_polygons(alpha = 0.1) +
tm_shape(gwr_sf_adaptive) +
tm_dots(col = "AREA_SQM_TV",
border.col = "gray60",
border.lwd = 1) +
tm_view(set.zoom.limits = c(11,14))
tmap_arrange(AREA_SQM_SE, AREA_SQM_TV,
asp=1, ncol=2,
sync = TRUE)Warning: The shape mpsz is invalid (after reprojection). See sf::st_is_valid
Warning: The shape mpsz is invalid (after reprojection). See sf::st_is_validtmap_mode("plot")tmap mode set to plottingBy URA Plannign Region
tm_shape(mpsz[mpsz$REGION_N=="CENTRAL REGION", ])+
tm_polygons()+
tm_shape(gwr_sf_adaptive) +
tm_bubbles(col = "Local_R2",
size = 0.15,
border.col = "gray60",
border.lwd = 1)Warning: The shape mpsz[mpsz$REGION_N == "CENTRAL REGION", ] is invalid. See
sf::st_is_valid